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Default Goal Seek with Complex Numbers

Hello;

I'm trying to understand how complex numbers are handled/processed in Excel.
As related to my application, an interesting exercise would be to use Goal
Seek w/s command to find the roots of the equation:
X^2 + 4 = 0
setting the value (rounded) in cell A2 to 0 by changing A1
A1:: 1+i
A2:: =COMPLEX(ROUND(IMREAL(IMSUM(IMPOWER(A1,2),4)),6),
ROUND(IMAGINARY(IMSUM(IMPOWER(A1,2),4)),6))

Obviously a conventional/direct use of Goal Seek wouldn't work since Excel
treats complex numbers as text.

Perhaps, one should use Goal Seek twice in this case:
first: find the coefficient "a" for IMREAL(A2) = 0
second: find the coefficient "b" for IMAGINARY(A2) = 0
and the root would be "a+bi".

There might be an easier way to do it. Any suggetion ??
(Excel 2003 SP2, Windows XP)

Thank you kindly.
 
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